PRACTICAL PROBLEMS

1. A man's salary is $950 per year. He pays $260 for board, $136 for clothing, and $115.75 for other expenses. How much has he left?

2. A grocer opened an account and deposited in bank during the week the following sums: $495.65, $305.75, $693.29, $75.80, $243.89, and $375.77. He then had a balance to his credit of $1200.15. How much had he withdrawn?

NOTE. First estimate the result mentally, as follows: $500+ $300+$700 + $75 + $250 + $375 = $2200;$2200 $1200 = $1000, approximate answer. Then find the exact result and compare the answers.

3. What is the value of 25 freight cars at $ 476 each? NOTE. As 25 is 4 of 100, multiply 476 by 100 by adding two naughts, and divide the product by 4.

4. A woman sold at a store 16 doz. eggs at 18¢ a dozen and 134 lb. butter at 28 a pound. How much did she receive?

SOLVING PROBLEMS

Tell what is given in each problem, what is required, and the process by means of which each step of the problem may be solved.

When possible estimate results mentally and compare with exact answers to written work.

1. A butcher paid $1476 for 41 head of cattle. How much was that per head?

NOTE. Estimate the cost per head mentally as $1500÷40. Compare the result with the exact answer.

2. I bought 52 yards of cloth at 25¢ a yard, and 16 yards of matting at 28¢ a yard. Find the cost of both.

NOTE. Estimate the cost mentally as 4 of $52 plus 15 × 30¢. Then work the example and compare answers.

3. At 38¢ a word, how many words can I cable from New York to Sweden for $3.04?

.

4. A lady sold 6 doz. eggs at 18 cents a dozen, and 8 lb. of butter at 27 cents a pound. How much did she receive for both?

5. A farmer bought 4 horses at $137 each, 7 cows at $27 each, and 38 sheep at $6.50 each. Find the cost of all.

6. What will be the cost of 108 lb. of ham at 16 cents a pound, and 48 lb. of bacon at 18 cents a pound? 7. A man paid $165 for a carriage, and 3 times as much for a horse. How much did he pay for both?

SOLVING PROBLEMS

1. A dairyman has 137 cows in one herd and 47 less in another. How many cows has he?

137 No. cows in one herd.

47 No. less in 2d herd.

90 No. cows in 2d herd.

137 cows +90 cows=227 cows.

Study of Problem

1. What is given in this problem?

a. The number of cows in one herd.

b. The difference in the number in the two herds.

2. What is required in the problem?

a. The number in the second herd.

b. The number in both herds.

3. How can you find what is required from what is given ?

a. By subtracting the difference from the number in the first herd.

b. By adding the number of cows in the two herds.

MENTAL ESTIMATE: 140 - 50 = 90; 140 + 90 = 230, approxi

mate answer.

NOTE. The purpose of these studies is: (1) To train the pupil to understand the conditions of the problem. (2) To lead him to discover the logical steps in the solution of the problem. (3) To place emphasis upon the development of mathematical power.

2. A man has 267 sheep in one field and 88 less in another. How many sheep has he?

3. A merchant has $ 496 in the safe and $ 175.25 less in the bank. How much money has he in both places? 4. A man sold a farm for $7625 and gained $1685. How much would he have received for it if the gain had been $2675?

SOLVING PROBLEMS

i. A man earned each day in one week as follows: $2.75, $3.65, $4.75, $6.75, $1.75, $12.75. Find his average daily earnings.

2. Two men contribute equal amounts to buy a lot for $875; to build a storeroom for $4860; for furniture, $520; and for goods to begin business, $5785. How much does each pay?

3. A creamery received milk for six days as follows: 7640 gallons, 8675 gallons, 9634 gallons, 8432. gallons, 8763 gallons, and 8604 gallons. What were the average daily receipts?

4. If Helen received 85 in arithmetic, 79 in grammar, 89 in history, 92 in geography, 86 in physiology, and 85 in writing, what was her average in these studies?

5. The attendance at a school was 604 on Monday, 607 on Tuesday, 598 on Wednesday, 603 on Thursday, 598 on Friday. What was the average daily attendance for the week?